208 • Mr. C. H. Lander on Struts and Tie-Rods 



girder, and if M a and M 6 represent the fixing moments at 

 each end of the encastre beam, then 



M _A(c + 3z) 



""" 2c 2 



A(c-3*) . 



where 



c = the semi-span; 



z = distance of centre of gravity of free-ended 

 bending moment diagram from centre of 

 beam ; 



A = area of free-ended bending moment diagram ; 



and the true bending moment diagram is obtained by setting- 

 up a base-line which is at a distance M a above the base-line 

 for the free-ended bending moment diagram at one end, and 

 a distance M 6 above at the other. If A-i be now taken as the 

 area of the deflexion curve and z 1 to be the distance of 

 the centre of gravity of the primary deflexion curve from 

 the centre of the span, the true base-line from which the 

 moments exerted by the endlong load should be measured is 

 obtained by setting up ordinates at each end of the span 

 equal to M a ' and M 6 ' where M a ' and M 6 ' are obtained from 

 the above formula. 



Beam with Lateral Loading and End Load continuous over 

 ■several supports. — An important case of continuous beams 

 with end loadings occurs in the case of aeroplane spars, 

 particularly of the monoplane class where a light wood or 

 metal spar is attached at one extremity to the fuselage of 

 the machine and braced at intervals along its length by 

 wires attached to the chassis. 



Before the application of the method to beams of this 

 type can be properly considered, it is necessary to consider 

 shortly the means by which the bending moment diagram of 

 continuous beams for lateral loads only may be drawn. The 

 most convenient of the several methods of effecting the same 

 purpose is that due to Claxton Fidler *, who makes use of 

 what he has called the " characteristic points 5 ' of the bending 

 moment diagram. 



* For a full account of this method so far as it affects the solution of 

 beams continuous over several supports and loaded in any manner but 

 without end loading, the reader is referred to ' Bridge Construction,' 

 by Claxton Fidler, chapter ix. 



